Trouble getting video as plane to show it's image
I really won't recommend the method you are going with it is seriously troublesome and tiring. I would say use blender's built-in Video editor. You can create the effects as separate projects. In the project, go to render settings and go to film and click transparent or transparency (depending on the version you are using). Something like this:

After rendering this in OpenEXR format. The thing is most video codecs don't support alpha channels and the ones that do, aren't available in blender. So you can take the image files, plop them into the video editor built-in blender or use some 3rd party-software like kdenlive or Davinci Resolve. You can take the video file and the effects file and it will work.
Alternatively, if you still insist on using it as a background image/video. DO this. Click on the camera and go to the camera settings. Enable background images and click on the dropdown. There, click add image and click on the open button. The file explorer should pop-up and then locate and select the video file. It will come as the background video and you can happily throw in whatever effects you want. Here's the video edition of the method (WARNING: This is not the total tutorial about what you want but shows a few steps on this method and you may find this helpful):
https://www.youtube.com/watch?v=kfGXRsaBf5U
I would personally go with the 1st method but you can go with the one you prefer. Hope it helps.
P.S I also found another QnA that is related to your problem. Check it out. Link's below:
Movie Clip On Plane